35503 ÷ 7 = 5071 R6
Alright, let's work through the division of 35503 by 7 step by step.

Step 1:
7 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 7

Step 2:
7 goes into 35 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 35 from 35 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 7

Step 3:
7 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 50
Subtract 0 from 5 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 7

Step 4:
7 goes into 50 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 507
Subtract 49 from 50 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 7

Step 5:
7 goes into 13 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 5071
Subtract 7 from 13 to get 6.

The final result is 5071 with a remainder of 6.